Wisdom they considered as superior to virtue, as being connected with the contemplation of the upper and purer regions, while virtue was conversant only with the sublunary part of the world. Happiness, they thought, consisted in the science of the perfection of the soul; or in the perfect science of numbers; and the main object of all the endeavours of man was to be, to resemble the Deity as far as possible.

Alcmæon of Crotona was a pupil of Pythagoras; but that is all that is known of his history. He was a great natural philosopher; and is said to have been the first who introduced the practice of dissection. He is said, also, to have been the first who wrote on natural philosophy. Aristotle, however, distinguishes between the principles of Alcmæon and Pythagoras, though without explaining in what the difference consisted. He asserted the immortality of the soul, and said that it partook of the divine nature, because, like the heavenly bodies themselves, it contained in itself th